Obviously, the records need to be reordered along with being renumbered. As far as I can tell, the above "solutions" don't work.

use strict;
use warnings;

my ($c, %hash);
$_ = join '', <DATA>;
$hash{$1} = $2 while m/"(\d+)"(.*?{.*?})/gs;
print "\"".++$c."\"$hash{$_}\n" for sort {$a <=> $b} keys %hash;

__DATA__
"1"
{
     "time: 1247";
     "sump:  15";
}
"2"
{
     "time: 1255";
     "sump:  9";
}
"8"
{
     "time: 1350";
     "sump:  7";
}
"5"
{
     "time: 1600";
     "sump:  3";
}
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